2 The observations, measurements and reductions

All observations were made at the Cassegrain-focus of the 1.6 m Ritchey-Chretien reflector of the Laboratório Nacional de Astrofísica at Brazil (geographical longitude: $-3^{\rm h}\ 02^{\rm m}\ 19^{\rm s}$, latitude: $-22^\circ\ 32\hbox{$^\prime$}\ 04\hbox{$^{\prime\prime}$}$ and altitude: 1872 m). The focal length of the Cassegrain combination is 15.8 m, which results in a plate scale of $13''\!$/mm at the focal plane.

Photographic plates with Kodak emulsions IIaO, 103aO, IIaF and IIIaJ and with dimensions $26\times21$ arcmin² were used. All plates were hyper-sensitized and the exposure times have varied from 3 to 15 minutes. The long exposure times for many plates (57% have 10 or 12 minutes of exposure time) were used since the initial goal was to observe the faint satellites in the Lagrangian points of Thetys and Dione. The positions for these satellites will be published in a forthcoming paper. No filter was used. Figure 1 presents one of our images of the Saturn's system. In the figure in order to bring up the images of the faint satellites near Saturn, a gradient filter was used.

  

Figure 1: Region of a photographic plate taken at 07/30/1988, $1^{\rm h}\ 19^{\rm m}\ 0^{\rm s}$ UT. The emulsion is IIao and the exposure time was $3^{\rm m}$. The distance of Iapetus from Saturn is 8$^\prime$ 35$^{\prime\prime}$ in the East direction. Therefore, it is not in this region of the plate. For the same reason, the GSC stars cannot be seen

Our images of Saturnian system present some peculiar features. All Saturn images are saturated and not measurable. The images of Titan and Rhea are also saturated on the long exposure time plates. To avoid the diffraction cross in these saturated images, an eight round apertures mask was placed between the secondary mirror supporting vanes. For the plates taken with long exposure time, the images of Mimas and Enceladus are immersed in the light scattered by the planet and its bright rings. For many plates, the images are elongated probably due to guiding problems.

The number of positions of Mimas is smaller than those for the other satellites. This satellite is very difficult to observe due to its small distance from the planet and the bright rings. Table 1 presents the number of Titan's referred positions and the number of observed nights are presented for each satellite. Figure 2 shows the histogram of the number of plates with respect to the epoch of the observations. Each bar corresponds to one of the 12 observational missions.

  

Table 1: Number of positions referred to Titan and of observed nights for Saturn satellites. The total number of observed plates and nights are 138 and 30, respectively

  

Figure 2: Histogram of the photographic plates of Saturn with respect to time. Each bar corresponds to an observational mission

The digitized images of the satellites and stars were obtained with the PDS 1010A of the Observatório Nacional-Brazil. For the image scans a square slit which side had 20$\mu$ was used. To find the center of these digitized images, the ASTROL routines package (Colas & Serrau 1993) was employed. A two-dimensional Gaussian fitting on a small circular area around the image, in which the background was removed by a second-degree polynomial, was used to determine each center. The errors upon the centering procedure where at 0$.\!\!^{\prime\prime}$01 for the satellites and field stars, while at 0$.\!\!^{\prime\prime}$02 for Mimas. To ensure a robust centering for Mimas images, the image position has been computed for 10 different centers of circular area around the satellite. The differences between the computed positions were smaller than 0$.\!\!^{\prime\prime}$01.

The astrometric calibration was performed using the method presented in Vieira Martins et al. (1996) (see also Assafin et al. 1997). It consists on the setting of an astrometric catalogue for the stars on the plate, using the Guide Star Catalogue (GSC) corrected by the PPM Catalog. It can be remarked that, by they relative nature, the present astrometric determinations would not be improved through a Hipparcos tied GSC correction. The mean number of GSC measurable stars around Saturn was 24 per plate. However, for some plates we have few GSC measurable stars or they were not well distributed around Saturn. For every plate, the RMS of the residuals for the plate stars is about 0$.\!\!^{\prime\prime}$16 in the right ascension and declination directions. In order to evaluate the accuracy of the astrometric calibration, we compared the equatorial coordinates of GSC stars, plate by plate, in a same mission. The RMS of the differences is around 0$.\!\!^{\prime\prime}$07. The difference between these errors indicates that an important source of errors is just the bad theoretical positions of the GSC stars positions.

  

Figure 3: Histogram for the right ascension (X) and declinations (Y) residuals of the Saturnian satellites referred to Titan

 

Figure 3: continued

 

Figure 3: continued

 

Figure 3: continued

 

Figure 3: continued

 

Figure 3: continued

 

Figure 3: continued

The theoretical positions of Saturn were calculated using DE403 (Standish et al. 1995). To compute the light travel time the topocentric distance from the center of Saturn was adopted, since the error on the satellite position due to this approximation is smaller than 0$.\!\!^{\prime\prime}$006 (Harper & Taylor 1994). However, for Iapetus the topocentric distance of the satellite was used.

In Table 2 (accessible in electronic form) are listed our positions of the Saturn satellites related to Titan. The data are presented in the same format used in the catalogue of Strugnell & Taylor (1990). The reference system is defined by the mean equator and equinox J2000.